Lattice is a way of discretizing a quantum field theory for numerical simulations.
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Lattice model completely constrained by boundary data
I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole ...
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$SU(N)$ Neel manifold
I have seen multiple papers talking about the manifold, $M$ of the Neel order for an $SU(N)$ magnet is
$$M~=~\frac{U(N)}{U(m)\times U(N-m)}.$$
So for instance, a $SU(2)$ magnet has manifold
$$M ~=~ ...
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1answer
170 views
Expansion in solid spherical harmonics on the lattice
I'm interested in calculating scattering processes (e.g. Coulomb scattering of an electron beam by a single ion) in the context of lattice quantum field theory, and wonder if there is something like ...
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What symmetries does a lattice calculation need to preserve?
I've heard that it is impossible to have a properly Lorentz-invariant lattice QFT simulation, as the Lorentz invariance is spoiled by the nonzero lattice distance $a$. I've also heard that there are ...
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2answers
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How local is the stress tensor?
I am confused by the definition of the stress tensor in a crystal (let's say a semi-conductor), I don't see how it could be "more local" than over an unit cell. I know that in field theory the stress ...
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Orientation in GaAs
I can't find the precise definition of what is the orientation of a GaAs lattice. Being the superposition of two fcc lattices (one of Ga, the other of As), I would think that it is the direction of ...
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Chiral coupling in string-nets
In Xiao-Gang Wen's review of topological order http://arxiv.org/abs/1210.1281 , he states in footnote 52 that string-nets are so far unable to produce the chiral coupling between the SU(2) gauge boson ...
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Origin of Laue equations?
The Bragg condition (by Bragg in 1913) can be derived by the Laue equations that is making use of the Miller indices and all the latice/crystal stuff (so basically it's bringing Bragg's law to more ...
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Laue diffraction/equations: Path difference, why a minus sign and not a plus?
The Laue diffraction (that reduces to the Bragg refraction in the end) has for the path difference of the incoming and outgoing beam
$$\Delta s = \vec R \cdot ( \vec k_0/k_0 - \vec k^\prime/k^\prime ...
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phi^4 theory on lattice
I was reading the lecture notes from
http://nic.desy.de/sites2009/site_nic/content/e44192/e62778/e91179/e91180/hmc_tutorial_eng.pdf
I am a little bit confused how points on the lattice gets assigned ...
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2answers
288 views
What is a bulk phase transition?
I have been able to google "bulk phase transition" and get plenty of results that verify that something called a bulk phase transition exists, however, I cannot seem to find a precise definition of ...
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SU(2) critical point and volume dependence
I am doing multi-dimensional plots of $\beta_j$ for SU(2) for infinite volume to understand the flow behavior and I was wondering, before I go too much further, if anyone knew off the top of their ...
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2answers
117 views
Pair interactions on finite square lattice
I am looking for an exact or approximate solution to a statistical lattice-particle problem:
Given a lattice of size $L\times L$ where $\rho\cdot L^2$ particles are randomly distributed, calculate ...
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2answers
124 views
Graph Invariants and Statistical Mechanics
Many intuitive knot invariants including Jones' polynomial are inspired by statistical mechanics. Further profound connections have been explored between knot theory and statistical mechanics. I was ...
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1answer
104 views
Why are topological solitons present in some phases for lattice models?
Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
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Discrete sum over an exponential with imaginary argument, considering only every second lattice site?
Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g.,
A-A-A-...-A-A (total of N sites)
...
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Is the U(1) gauge theory in 2+1D dual to a U(1) or an integer XY model?
The compact U(1) lattice gauge theory is described by the action
$$S_0=-\frac{1}{g^2}\sum_\square \cos\left(\sum_{l\in\partial \square}A_l\right),$$
where the gauge connection $A_l\in$U(1) is defined ...
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189 views
How to determine if an emergent gauge theory is deconfined or not?
2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are ...
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One-Plaquette Action and SU(2)'s Irreducible Representations
I have a typical single-plaquette partition function for a gauge-field
$$ Z=\int [d U_{\text{link}}] \exp[-\sum_{p} S_{p}(U,a)]$$
with $U$ as the product of the the $U$'s assigned to each link around ...
3
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1answer
141 views
Why does the creation operator take a continuum value for the momentum?
Imagine that you have a lattice and a set of masses. Each mass at a lattice point. Now each two neighbouring masses are connected with spring.
Now in Classical Mechanics (CM) the ground state is the ...
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2answers
99 views
Dilation invariant lattice
In one dimension, we can define the lattice $ f(x+a)=f(x) $ so the lattice is translation invariant.
But, can we give a lattice so $ f(p^{k}x)=f(x) $ for ALL the primes $ P= 2,3,5,7,11,....$ and ...
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79 views
Consideration of static atomic displacements in electronic structure calculations
I am hoping to discuss some details of electronic structure calculations. I am not an expert on this topic, so please forgive any abuse of terminology. It is my understanding that first principles ...
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143 views
detail procedure of numercal calculation
I need a help.
I am looking for a reference to show me detail procedure of numercal calculation a physical quantity on Lattice. I have knowlegde of physics part or I find it. My problem is calculation ...
8
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1answer
86 views
What evidence do we have for S-duality in N=4 Super-Yang-Mills?
Do we have anything resembling a proof*? Or is it just a collection of "coincidences"?
Also, do we have evidence from lattice gauge theory computations?
*Of course I'm not talking about a proof in ...
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Are there rigorous constructions of the path integral for lattice QFT on an infinite lattice?
Lattice QFT on a finite lattice* is a completely well defined mathematical object. This is because the path integral is an ordinary finite-dimensional integral. However, if the lattice is infinite, ...
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141 views
Why is the crystallography restriction obeyed?
The crystallography restriction states that any 2-dimensional lattice can have rotational symmetry of degree 1, 2, 3, 4 or 6 - and that's it. A simple proof of I've heard of this is: the magnitude of ...
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166 views
Continuum theory from lattice theory
I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
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2answers
232 views
Why can't we set the lattice spacing 'a' in lattice QCD?
My question is to do with lattice QCD. In the lattice action there is a parameter, 'a', the lattice spacing in physical units.
However, if we want to generate a configuration with a certain lattice ...
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2answers
692 views
What is the fundamental reason of the fermion doubling?
Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds ...
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229 views
Lattice QCD and the 5th dimension
I was digging into Nielson-Ninomiya Theorem and doubler fermions, as well as solutions to these problems using Domain Wall Fermions and overlap lattice fermions, both of which make effective use of a ...
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4answers
429 views
Home-made lattice calculation?
The topic of Lattice QCD or Lattice gauge theory or even Lattice field theory is quite old now. And the main reason for the interest in the topic is the ability to calculate nonperturbative stuff on a ...
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1answer
175 views
Convergence of periodic single fermion operators
First, a quick remark: I'm a mathematician, now working on some problems coming from physics (in particular Ising models on quasiperiodic chains). A few things I find rather mysterious. I would ...
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3answers
760 views
Why is high temperature superconductivity so hard to solve?
The phenomenon of high temperature superconductivity has been known for decades, particularly layered cuprate superconductors. We know the precise lattice structure of the materials. We know the band ...
2
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1answer
480 views
Lattice QCD and string theory
I've heard the claim that some aspects of string theory are used to improve Monte-Carlo simulations of lattice QCD, for example by people working at the LHC.
I know a bit about Monte-Carlo methods in ...
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1answer
189 views
Why do regular lattice elements heat up faster?
For example iron. A metal spoon heats up much quicker than a wooden/plastic one.
Why?
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290 views
What is known about some massive Gaussian models on a lattice?
Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle ...
